1. Field of the Invention
The present invention relates to a system which divides a signal such as an audio signal or a video signal into plural frequency bands and applies processing such as transmission or recording/reproduction on the band-division signals.
2. Description of the Prior Art
In the case where the transmission frequency bandwidth is narrower than the bandwidth of the original signal to be transmitted or a hierarchical application is required, the original signal is transmitted or recorded/reproduced after being divided into plural frequency bands. As such a technique, there is known a sub-band coding. FIG. 7 schematically shows the sub-band coding. As shown, an original signal S is divided by a Low Pass Filter (LPF) 1 and a High Pass Filter (HPF) 2 into a low frequency band signal SL and a high frequency band signal SH. Subsequently, the low frequency band signal SL and the high frequency band signal SH are down-sampled by the factor 2 (i.e., by a sampling frequency which is 1/2 of that of the original signal S) by down-samplers 3 and 4, respectively, so that the total data amount of the two divided signals, i.e., the signals SL and SH, coincides with that of the original signal S. The low frequency band signal SL and the high frequency band signal SH thus obtained are transmitted by the transmission system 5. At the receiving side, up-samplers 6 and 7 up-sample the low frequency band signal SL and the high frequency band signal SH, respectively, to make the sampling frequency of them twice higher, and a LPF 8 and a HPF 9 eliminate aliasing noise. The low frequency signal SL' and the high frequency signal SH' thus obtained are added to each other to obtain a signal S' which is substantially identical to the original signal S. In the case that the system at the receiving side has an ability to reproduce only the low frequency band signal, it may reproduce only the low frequency band signal SL'. Thereby a hierarchical application may be achieved.
In the signal transmission using the band-division technique, there generally are following requirements. First requirement is that the original signal is desired to be completely re-synthesized, i.e., in the case of FIG. 7, the re-synthesized signal S' is completely identical to the signal S. The second requirement is that hierarchical application is ensured, i.e., the subband signal (normally the low frequency band signal) is reproducible independently.
However, in the method described above, the reproduced signal S' is not strictly identical to the original signal S due to the effect of aliasing noise introduced by the down-sampling. To overcome the problem raised by aliasing noise, there is proposed a method of using QMF (Quadrature Mirror Filter). QMF technique attempts to design the filter coefficients so that aliasing noise is canceled at the time of adding the band-divided signals to each other, thereby making it possible to suppress the effect of aliasing noise with the aid of this filter. However, even with the use of QMF, there is required a filter with a certain tap length (i.e., relatively many taps) to eliminate the effect of aliasing noise in a hierarchical application in which only the low frequency band signal is needed to be reproduced. Actually, since the tap length, the coefficient word length and the arithmetic word length are all finite in the hardware and/or software constituting the filter, it is impossible to make the reproduced signal S' completely and strictly identical to the original signal S. In other words, in order to achieve complete re-synthesizing of the original signal, sufficient arithmetic word length is required, and hence data amount to be processed increases considerably. This makes the system configuration complicated and the data amount to be transmitted or recorded may also increase considerably. On the other hand, limiting the operation word length to some extent disables the complete reproduction of the original signal.
In order to achieve complete re-synthesizing of the original signal, there is known another technique using SSKF (Symmetric Short Kernel Filter), which includes short tap-length analysis synthesizing filter.
However, in this case, the frequency characteristic of the filter is not very steep due to its short tap-length, and hence aliasing noise by the downsampling increases. Therefore, this technique is not applicable to a hierarchical system which needs the reproduction of only the low frequency band signal.